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Math Help - Circular cylinder area.

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    Circular cylinder area.

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    assuming "largest" is in terms of volume ...

    sketch the circle x^2 + y^2 = 2^2

    inscribe a rectangle in the circle ... rotation of the figure about the y-axis yields a cylinder inscribed in a sphere of radius 2.

    volume of a cylinder, V = \pi r^2 h

    V = \pi x^2 \cdot 2y = \pi x^2 \cdot 2\sqrt{4 - x^2}

    find \frac{dV}{dx} and find the values of x and y that maximize the volume ... then determine the surface area,

    A = 2\pi r^2 + 2\pi rh = 2\pi x^2 + 2\pi r (2y)
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